How many dogs can one person watch at a time?

Rover doesn't make any rules about such things as every sitter here is independent and leaves it up to the customer to evaluate the suitability of potential sitters. That is why there are profiles, which do specify the number of animals a sitter accepts for boarding, and why you are encouraged to conduct a Meet & Greet with the sitter, where you can view the facility.

In Rover's Terms of Service, it states:

2.2 Rover does not provide Pet Care Services.. Rover is a neutral venue for Service Providers and Pet Owners. Rover is not a Service Provider and, except for emergency phone support and other resources and support specifically described in the Rover Service, does not provide pet care services. We make no representations or warranties about the quality of boarding, pet sitting, dog walking, house sitting, or other services provided by Service Providers (“Pet Care Services”), or about your interactions and dealings with users. Service Providers listed on Rover are not under the direction or control of Rover, and Service Providers determine in their own discretion how to provide Pet Care Services. Though we provide general guidance on our Site to Service Providers about safety and pet care and to Pet Owners about selecting and engaging Service Providers, Rover does not employ, recommend or endorse Service Providers or Pet Owners, and, to the maximum extent permitted by applicable law, we will not be responsible or liable for the performance or conduct of Service Providers or Pet Owners, whether online or offline. We conduct an initial review of Service Provider profiles and we facilitate Background Checks or Identification Verifications (each as described in Section 10, below) on Service Providers conducted by a third party, but, except where explicitly specified in the Rover Service (and then only to the extent specified), do not otherwise screen Service Providers or Pet Owners. You should exercise caution and use your independent judgment before engaging a Service Provider, providing Pet Care Services, or otherwise interacting with users via the Rover Service. Pet Owners and Service Providers are solely responsible for making decisions that are in the best interests of themselves and their pets.

https://www.rover.com/terms/tos/

Since I have no way of knowing where you are located and the sitter that you used, taking in that many animals would qualify as a kennel rather than a home boarding situation. Typically local zoning laws dictate the requirements for such facilities. Rover's position is that the Service Provider is responsible for ascertaining legal requirements.

If the sitter's profile misrepresented the nature of the service provided, then I would encourage you to contact Rover's Customer Support at [Edit: Rover’s contact options have changed. Visit the Rover Help Center at https://support.rover.com/ to find the phone number, help articles, or chat with the team].

It depends on the person taking care of them. I take in 1 dog at a time due to the size of the house. In a bigger space I take in dogs that come in a pair from the same owner. That is the max I would do on my own.